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Sean B = {(2, −1), (1, 1)} y D = {x ^ 2, x + 1, x−1} bases de R2 y R2[x] respectivamente?

Sean B = {(2, −1), (1, 1)} y D = {x ^ 2, x + 1, x−1} bases de R2 y R2[x] respectivamente. Determinar [F]D, B, si F : R2 →R2[x] es una T. L. tal que F (2, −1) = x2 −1 yF (3, 0) = x ^ 2 + x + 2.

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Reinius
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<img src="https://tex.z-dn.net/?f=F%282%2C-1%29%3Dx%5E2-1%5C%5C%0AF%283%2C0%29%3Dx%5E2%2Bx%2B2%5C%5C%20%5C%5C%0A%5Ctexttt%7BFaltar%5C%27ia%20encontrar%20%7DF%281%2C1%29%5Ctexttt%7B%2C%20pongamos%20que%20sea%3A%7D%5C%5C%20%5C%5C%0AF%281%2C1%29%3DaF%282%2C-1%29%2BbF%283%2C0%29%5C%5C%20%5C%5C%0AF%281%2C1%29%3Da%28x%5E2-1%29%2Bb%28x%5E2%2Bx%2B2%29%5C%5C%20%5C%5C%0AF%281%2C1%29%3D%28a%2Bb%29x%5E2%2Bbx-a%2B2b%5C%5C%20%5C%5C%0A%5Ctexttt%7BPor%20otro%20lado%3A%20%7D%5C%5C%20%5C%5C%0AF%281%2C1%29%3DaF%282%2C-1%29%2BbF%283%2C0%29%5C%5C%20%5C%5C%0AF%281%2C1%29%3DF%282a%2C-a%29%2BF%283b%2C0%29%5C%5C%20%5C%5C%0AF%281%2C1%29%3DF%282a%2B3b%2C-a%29%5C%5C%20%5C%5C%0A2a%2B3b%3D1%5Cwedge%20a%3D-1%20%5Cto%20a%3D-1%5Cwedge%20b%3D1%5C%5C%20%5C%5C%0AF%281%2C1%29%3Dx%2B3%5C%5C%20%5C%5C%0AF%28p%282%2C-1%29%2Bq%281%2C1%29%29%3Dp%28x%5E2-1%29%2Bq%28x%2B3%29%5C%5C%20%5C%5C%0AF%28p%282%2C-1%29%2Bq%281%2C1%29%29%3Dpx%5E2%2Bqx%2B%283q-p%29%0A" /> <img src="https://tex.z-dn.net/?f=F%28p%282%2C-1%29%2Bq%281%2C1%29%29%3Dpx%5E2%2B%5Cleft%28%5Cdfrac%7B4q-p%7D%7B2%7D%5Cright%29%28x%2B1%29%2B%5Cleft%28%5Cdfrac%7Bp-2q%7D%7B2%7D%5Cright%29%28x-1%29" />.

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Americana1927
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